completely integrable system
1Integrable system — In mathematics and physics, there are various distinct notions that are referred to under the name of integrable systems. In the general theory of differential systems, there is Frobenius integrability, which refers to overdetermined systems. In… …
2LTI system theory — or linear time invariant system theory is a theory in the field of electrical engineering, specifically in circuits, signal processing, and control theory, that investigates the response of a linear, time invariant system to an arbitrary input… …
3Dynamical system — This article is about the general aspects of dynamical systems. For technical details, see Dynamical system (definition). For the study, see Dynamical systems theory. Dynamical redirects here. For other uses, see Dynamics (disambiguation). The… …
4Nonholonomic system — A nonholonomic system in physics and mathematics is a system whose state depends on the path taken to achieve it. Such a system is described by a set of parameters subject to differential constraints, such that when the system evolves along a… …
5Constant of motion — In mechanics, a constant of motion is a quantity that is conserved throughout the motion, imposing in effect a constraint on the motion. However, it is a mathematical constraint, the natural consequence of the equations of motion, rather than a… …
6Linear flow on the torus — In mathematics, esecially in the area of mathematical analysis known as dynamical systems theory, a linear flow on the torus is a flow on the n dimensional torus:mathbb{T}^n = underbrace{S^1 imes S^1 imes cdots imes S^1} nwhich is represented by… …
7Frobenius theorem (differential topology) — In mathematics, Frobenius theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an overdetermined system of first order homogeneous linear partial differential equations. In modern geometric terms …
8Integrability conditions for differential systems — In mathematics, certain systems of partial differential equations are usefully formulated, from the point of view of their underlying geometric and algebraic structure, in terms of a system of differential forms. The idea is to take advantage of… …
9List of nonlinear partial differential equations — In mathematics and physics, nonlinear partial differential equations are (as their name suggests) partial differential equations with nonlinear terms. They describe many different physical systems, ranging from gravitation to fluid dynamics, and… …
10Exact solutions in general relativity — In general relativity, an exact solution is a Lorentzian manifold equipped with certain tensor fields which are taken to model states of ordinary matter, such as a fluid, or classical nongravitational fields such as the electromagnetic field.… …
